Question: What is the greatest common factor of $8m^{2}$, $4m$, and $10m^4$ ?
Answer: Let's factor each monomial to its prime factors: $\begin{aligned} 8m^{2}&=(2)(2)(2)(m)(m) \\\\ 4m&=(2)(2)(m) \\\\ 10m^{4}&=(2)(5)(m)(m)(m)(m) \end{aligned}$ We want the largest set of factors that's included in all three monomials. All of the monomials have one factor of $ {2}$ and one factor of $ m$ : $\begin{aligned} 8m^{2}&=(2)(2)(2)( m)(m) \\\\ 4m&=(2)(2)( m) \\\\ 10m^{4}&=(2)(5)( m)(m)(m)(m) \end{aligned}$ This is the greatest common factor: $( {2})( m)=2m$